Try to stay on the side with the least amount of mice, because even if the platform tips, you will have the highest chance of survival if you head toward the center. If you're caught on the heavier side when this happens, you might not be able to wall jump since the ground underneath the dynamic platform is transparent. Switch sides if yours starts to descend, and once you have the cheese, make a mad dash for the hole. Don't stay in the middle - there is no shaman who will help you.
There is no shaman on this map.